He said it with a rueful smile. Lord O’Donnell reckons that private sector executives are not always as good as they are cracked up to be by some ministers. “I tried to bring in more people from outside and on the whole they did slightly worse than other civil servants,” he told a seminar on leadership at the Institute for Government (IfG) in London. “Often they took very big pay cuts to come in. You’d see some of them and you’d think… what was all that about?”

Lord O’Donnell’s comments raise an issue that is fast becoming a hot potato. The role of the private sector in running our public services and even advising ministers has caused a row in the Cabinet. There are suggestions it is also causing rifts among Lord O’Donnell’s successors (his job was split) – Sir Jeremy Heywood, the Cabinet Secretary, and Sir Bob Kerslake, the head of the Civil Service. The debate matters to all of us. Potentially it affects our daily dealings with officialdom and the quality of government policy.

The heated arguments have been triggered by the long-awaited Civil Service reform plan that was unveiled to the Cabinet this week by Francis Maude, the Cabinet Office Minister, and Sir Bob. The plan includes proposals for further Civil Service cuts and the outsourcing of some policy-making to management consultants, academics and think tanks. Radical stuff you may think, and so it seems to many in Whitehall – but not radical enough for some, notably Michael Gove, the Education Secretary, hence the spat in Cabinet. Apparently Mr Gove hankers after the slash-and-burn approach favoured by Steve Hilton, the Prime Minister’s controversial former policy guru. Mr Hilton has now retreated to California but he seems to have left a legacy of grief.

Behind the scenes there are reports – unconfirmed – that the politicians’ wrangling reflects similar dissension between Sir Bob and Sir Jeremy. Sir Bob, according to one insider, has been saying that Sir Jeremy is manipulative, too Sir Humphrey-like and “won’t look at the knitting”. Meanwhile, Sir Jeremy has been suggesting that Sir Bob has a lot to learn about Whitehall and that he is “doing his best at a new level”. This is seen by some as an argument between those who have management experience and those who do not. Sir Jeremy is a brilliant mandarin but he has never run a department. Mr Gove is a gutsy minister, but his previous career was as a scribbler on The Times. Sir Bob used to run Sheffield, and Mr Maude came to government with considerable business experience. Sir Jeremy, who publicly paid tribute to “my friend Steve Hilton”, is apparently keen to experiment, and is even said to distance himself a little from the rest of the Civil Service as “a way of getting ministers’ confidence”. Sir Bob dismissed Mr Hilton’s calls for 90 per cent Civil Service cuts as “nonsense”.

Where does all this leave the rest of us? The public should be wary of too much radicalism, of too much haste to hand over public services and policy-making to the private sector. For a start there is no guarantee that it will save money. Management consultants, the bane of Whitehall during the Blair years, could enjoy a resurgence. Rebadging themselves as “professional services”, they are likely to offer loss-leader prices to begin with and then raise their charges – after the Government’s in-house provision has been closed down.

Then there is the question of trust. Do we really want to pay our taxes to a private sector company which will want – quite reasonably – to make a profit on the task? Think of the way some local authorities outsourced clamping to private sector companies whose main aim was to maximise their own revenues rather than aid the flow of traffic. The prospect of further substantial cuts in Civil Service numbers may have drawbacks too. Do we want longer queues at airports?

Even outsourcing policy-making will be harder than it looks. Senior figures in Whitehall point out that it is not just a matter of a few wizard ideas. There is all the business of providing data, consulting people and drawing up legislation. And who would assess such policy proposals when they were presented? The Civil Service.

One thing the Government hopes to do is improve Whitehall’s management of major public sector projects. Nobody would disagree with the aim. At the IfG, Lord O’Donnell was asked by Bernard Jenkin, Tory chairman of the Commons public administration select committee, about the billions wasted on public sector projects, with nobody resigning or taking the blame and ministers and civil servants sheltering behind each other. Lord O’Donnell said there was a “straightforward” way to cope with this. The reason major projects went off track was because ministers wanted changes. If civil servants were to appear before MPs and take responsibility for major projects, he said, then they would need more power so that they could prevent constant changes in specifications. This would require “bold moves” by government. Giving officials power not just to say no, minister, but to stop their political masters doing what they wanted might be a step too far even for the most radical ministers.

As things are, unless ministers and mandarins get their acts together, reform plans are doomed.